Related works.
We survey relevant researches along two threads. The first thread studies UAV's energy-efficiency problem with either routing or speed scheduling optimization. For example, [1]} proposed the looking before crossing algorithm, which is proved to be optimal for the offline speed scheduling problem under a practical flight energy model. [2]} considers an energy-aware path planning algorithm that minimizes energy consumption while satisfying coverage and resolution constraints. Please refer to [3]} for a survey work. In contrast, we focus on theoretical issues of the problem especially when truck trips are released in an online fashion. We aim to unveil the adaptability of the "ride-sharing" in UAV travelling in the worst-case scenario, which is usually measured by online algorithms and competitive ratio [4]}.
The second thread focuses on classical combinatorial optimization problems. The \(k\) -server problem aims to efficiently move \(k\)  servers to serve a batch of online requests of the metric space  such that the total moving distance of all servers is minimized. The famous work function algorithm achieves a competitive ratio of \(2k-1\)  on general metrics and hence is optimal for 1-server problem on the line [5]}. When the server moves in constant velocity, the work function algorithm is optimal in achieving minimum completion time of serving all the online requests. A variant of the 1-server problem is the online repairman problem [6]} which asks for a tour that visits a set of online cities in the metric space such that the weighted sum of completion times of the cities is minimized. [6]} proposes a \((1+\sqrt{2})^2\) -competitive deterministic online algorithm for the general metric spaces and [8]} gave an improved 5.429-competitive algorithm for line metrics. A generalized version of the \(k\) -server problem is the \(k\) -taxi problem in which each request is represented by a pair \((s,t)\)  of two points (including the start point \(s\)  and end point \(t\) ) instead [9]}. In the gas station problem [10]}, a vehicle with a given tank capacity \(U\)  and an initial amount \(\mu _s\)  of gas, can purchase gas at each vertex of a complete graph at a certain price. And the objective of [10]} is to find
the cheapest way from a given start node \(s\)  to a given target node \(t\)  of the graph. Note that
the gas station problem involves neither the time constraint on vertices nor restrictions in the set of visited vertices. Another related problem is the online maximum \(k\) -interval coverage problem which aims to select \(k\)  online sub-intervals (i.e., truck trips) such that the total covered length of a target interval (i.e., the UAV's path) is maximized [12]}.
In contrast, the problem studied in this paper is more complicated since one has to face both the spatial and the temporal issues simultaneously and the power constraint of UAV travelling is further involved.
